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Information Logic of Galois Connections

Jouni Järvinen, Michiro Kondo, Jari Kortelainen, Jorma K. Mattila, Information Logic of Galois Connections. TUCS Technical Reports 853, Turku Centre for Computer Science, 2007.

Abstract:

<p>
In this paper, Information Logic of Galois Connections (ILGC) suited for approximate reasoning about knowledge is introduced.
Its axiomatization and Kripke-style semantics based on information relations is defined, and its completeness is proved.
It is also shown that ILGC is equivalent to the minimal tense logic Kt, and decidability of ILGC follows from this observation.
</p>

<p>
Additionally, relationship of ILGC to the modal logic S4 is studied. Namely, a certain composition
of Galois connection mappings forms a lattice-theoretical interior operator, and this motivates us to axiomatize a logic of these compositions.
The axiomatization resembles the one of S4, except that our logic is not `normal' in the sense that axioms N and K of S4 are not included in the set of axioms.
Finally, so-called interior model is introduced to define semantics and validity, and completeness of this logic is proved as well.
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BibTeX entry:

@TECHREPORT{tJaKoKoMa07a,
  title = {Information Logic of Galois Connections},
  author = {Järvinen, Jouni and Kondo, Michiro and Kortelainen, Jari and Mattila, Jorma K.},
  number = {853},
  series = {TUCS Technical Reports},
  publisher = {Turku Centre for Computer Science},
  year = {2007},
  keywords = {rough sets, fuzzy sets, approximate reasoning, knowledge representation},
  ISBN = {978-952-12-1987-0},
}

Belongs to TUCS Research Unit(s): Algorithmics and Computational Intelligence Group (ACI), FUNDIM, Fundamentals of Computing and Discrete Mathematics

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